Thawornkaiwong, Supachoke
(2012)
Statistical inference on linear and partly linear regression
with spatial dependence: parametric and nonparametric
approaches.
PhD thesis, The London School of Economics and Political Science (LSE).

Abstract

The typical assumption made in regression analysis with cross-sectional data is that of
independent observations. However, this assumption can be questionable in some economic
applications where spatial dependence of observations may arise, for example, from local
shocks in an economy, interaction among economic agents and spillovers.
The main focus of this thesis is on regression models under three di§erent models of
spatial dependence. First, a multivariate linear regression model with the disturbances
following the Spatial Autoregressive process is considered. It is shown that the Gaussian
pseudo-maximum likelihood estimate of the regression and the spatial autoregressive parameters can be root-n-consistent under strong spatial dependence or explosive variances,
given that they are not too strong, without making restrictive assumptions on the parameter
space. To achieve e¢ ciency improvement, adaptive estimation, in the sense of Stein (1956),
is also discussed where the unknown score function is nonparametrically estimated by power
series estimation. A large section is devoted to an extension of power series estimation for
random variables with unbounded supports.
Second, linear and semiparametric partly linear regression models with the disturbances
following a generalized linear process for triangular arrays proposed by Robinson (2011)
are considered. It is shown that instrumental variables estimates of the unknown slope
parameters can be root-n-consistent even under some strong spatial dependence. A simple nonparametric estimate of the asymptotic variance matrix of the slope parameters is
proposed. An empirical illustration of the estimation technique is also conducted.
Finally, linear regression where the random variables follow a marked point process is
considered. The focus is on a family of random signed measures, constructed from the
marked point process, that are second-order stationary and their spectral properties are discussed. Asymptotic normality of the least squares estimate of the regression parameters are
derived from the associated random signed measures under mixing assumptions. Nonparametric estimation of the asymptotic variance matrix of the slope parameters is discussed
where an algorithm to obtain a positive deÖnite estimate, with faster rates of convergence
than the traditional ones, is proposed.